54 Prof. H. A. Bowland on the 



is seen then to be in exact analogy with Newton's first Law 

 of Motion. Every time a material point does not move in a 

 straight line with constant velocity, that point is considered to 

 be acted on by force. Every time molecules or atoms assume 

 some steady state, which is not that the probability of which is 

 greatest, we will say they are compelled by force to do so. 



The relativity of the idea of force in molecular theory will 

 be perceived as clearly as it is in ordinary dynamics. 



VI. Notes on the Theory of the Transformer. 

 By Henry A. Kowland *. 



AS ordinarily treated the coefficient of self and mutual 

 induction of transformers is assumed to be a constant, 

 and many false conclusions are thus drawn from it. 



I propose to treat the theory in general, taking account of 

 the hysteresis as well as the variation in the magnetic perme- 

 ability of the iron f . 



The quantity p as used by Maxwell is the number of lines 

 of magnetic induction enclosed by the given conductor. 

 This will be equal to the number of turns of the wire into 

 the electric current multiplied by the magnetic permeability 

 and a constant. But the magnetic permeability is not a 

 constant but a function of the magnetizing force, and hence 

 we must write 



p = Bny + C (ny) 3 + B(nyf + &c. 



Where B, C, &c. are constants, n is the number of turns, 

 and y the strength of current. 



In this series only the odd powers of y can enter in order 

 to express the fact that reversal of the current produces a 

 negative magnetization equal in amount to the direct magne- 

 tization produced by a direct current. This is only approxi- 

 mately true, however, and we shall presently correct it by 

 the introduction of hysteresis. It is, however, very nearly 

 true for a succession of electric waves. 



To introduce hysteresis, first suppose the current to be 

 alternating so that y = c sin (bt + e), where t is the time and 

 e the phase. The introduction of a term A cos {bt + e) into 



* From the Johns Hopkins University Circular. Communicated by 

 the Author. 



t The problem is treated by the method of magnetic circuit first applied 

 by me to iron bars in my paper on " Magnetic Distribution" (Phil. Mag. 

 1875, 1. pp. 257, 348) and afterwards to the magnetic circuit of dynamos 

 at the Electrical Conference at Philadelphia in 1884. I also used the 

 same method in my paper on " Magnetic Permeability " in 1873 (Phil. 

 Mag. 1873, xlvi. p. 140). 



